The Pokémon Sword and Shield servers are currently down. If you try to connect to the online portion of the game, you will receive error code 2306-0811 and a message telling you that the servers are currently undergoing going maintenance.
Checking the Nintendo Service Status page shows that the servers are down for emergency maintenance, not scheduled maintenance, but this isn’t a surprise. The game has had some connection issues since launch, and disconnections have been pretty frequent for people while trying to play. People have also been experiencing some lag issues when online, and others have problems maintaining a steady connection when trying to trade Pokémon.
It is safe to assume that the servers will be down for at least a couple of hours longer, and we can hope this is because Nintendo and Game Freak are hard at work to get whatever backend issues have been affecting players all squared away. Depending on exactly how much work needs to be done, we could be waiting quite a while for the Pokémon Sword and Shield online servers to come back up.
At the moment, all you can do is wait for the servers to come back up. The good news is that Pokémon Sword and Shield do not require an online connection to play, and you can still go hunting for Pokémon and work on filling up your Pokédex. You won’t be able to play any of the online components while the service is down. You should even be able to take part in Max Raid Battles, but you will have to use AI teammates to do so instead of playing with other Trainers.